The present invention relates generally to MR imaging and, more particularly, to a system and method for correcting flow velocity measurements in phase contrast imaging using magnetic field monitoring.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, or “longitudinal magnetization”, MZ, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated and this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
Phase contrast measurement imaging is based on phase shifts accumulated by spins moving through magnetic field gradients. To account for field and susceptibility variations across the subject, two measurements with different velocity sensitivities are usually obtained. Ideally, phase subtraction of the two measurements cancels out any phase resulting from time-invariant magnetic field inhomogeneities such as susceptibility effects and phase contributions of stationary spins. Accordingly, the phase difference observed is expected to be linearly related to velocities in the object. In practice, however, residual phase errors result in a spatially-varying phase across the phase-difference image. Such phase errors may be induced by gradient switching, which causes eddy-current induced phase errors, and by phase errors related to magnetic fields concomitant to the actual gradient fields used for velocity encoding, also known as concomitant field induced phase errors.
Since any non-zero phase in the phase difference (or phase velocity) image corresponds to motion, accurate absolute measurements of velocity and flow are very difficult without effective baseline correction. One technique for baseline correction is performed by measuring the phase in an adjacent stationary structure and subtracting that mean baseline value from that in the primary vessel of interest. However, this type of correction is not possible if there are no adjacent stationary structures (such as in the heart) or when the background phase has substantial spatial variation.
Another technique is to perform a background phase correction to the image by fitting a linear, quadratic, or higher order spatial function to the image and using the fitted data to correct for the background variation in phase. This approach may include errors if there is a lack of appreciable stationary structures in the image. Furthermore, the spatial extent of the stationary structures may be limited, which adversely affects the precision of the fit. In addition, spatially-varying background phase may also be time-varying as a result of eddy current effects, which impacts the overall background phase in a phase difference or complex difference processed velocity image.
Gradient switching may induce eddy currents in the metallic structures of the scanner. Magnetic field distortions typically result if eddy currents are not fully blocked or if pre-emphasis currents are not properly adjusted. The eddy-current field opposes the initial gradient field and thereby decreases the desired rate of change. These effects increase with increasing gradient performance.
The time-dependent magnetic field can be decomposed into different orders of spatial variation:
                                          B            o                    ⁡                      (                                          r                ⇀                            ,              t                        )                          =                                            B              o                        ⁡                          (              t              )                                +                      x            ⁢                                          ⅆ                                                      B                    o                                    ⁡                                      (                    t                    )                                                                              ⅆ                x                                              +                      y            ⁢                                          ⅆ                                                      B                    o                                    ⁡                                      (                    t                    )                                                                              ⅆ                y                                              +                      z            ⁢                                          ⅆ                                                      B                    o                                    ⁡                                      (                    t                    )                                                                              ⅆ                z                                              +                                    1              2                        ⁢                          (                                                                    x                    2                                    ⁢                                                                                    ⅆ                        2                                            ⁢                                                                        B                          o                                                ⁡                                                  (                          t                          )                                                                                                            ⅆ                                              x                        2                                                                                            +                                                      y                    2                                    ⁢                                                                                    ⅆ                        2                                            ⁢                                                                        B                          o                                                ⁡                                                  (                          t                          )                                                                                                            ⅆ                                              y                        2                                                                                            +                                                      z                    2                                    ⁢                                                                                    ⅆ                        2                                            ⁢                                                                        B                          o                                                ⁡                                                  (                          t                          )                                                                                                            ⅆ                                              z                        2                                                                                            +                                  xy                  ⁢                                                                                    ⅆ                        2                                            ⁢                                                                        B                          o                                                ⁡                                                  (                          t                          )                                                                                                            ⅆ                      xdy                                                                      +                                  xz                  ⁢                                                                                    ⅆ                        2                                            ⁢                                                                        B                          o                                                ⁡                                                  (                          t                          )                                                                                                            ⅆ                      xdz                                                                      +                                  yz                  ⁢                                                                                    ⅆ                        2                                            ⁢                                                                        B                          o                                                ⁡                                                  (                          t                          )                                                                                                            ⅆ                      ydz                                                                      ⁢                                                                  +                …                                                                        (                  Eqn          ⁢                                          ⁢          1                )            where Bo(t) denotes the time-dependent, spatially-constant field;
            ⅆ                        B          o                ⁡                  (          t          )                            ⅆ      x        ,          ⁢            ⅆ                        B          o                ⁡                  (          t          )                            ⅆ      y        ,          ⁢            ⅆ                        B          o                ⁡                  (          t          )                            ⅆ      z      denotes the time-dependent, spatially linear gradient fields; and
                    ⅆ        2            ⁢                        B          o                ⁡                  (          t          )                            ⅆ              x        2              ,          ⁢                    ⅆ        2            ⁢                        B          o                ⁡                  (          t          )                            ⅆ              y        2              ,          ⁢                    ⅆ        2            ⁢                        B          o                ⁡                  (          t          )                            ⅆ              z        2              ,          ⁢                    ⅆ        2            ⁢                        B          o                ⁡                  (          t          )                            ⅆ      xdy        ,          ⁢                    ⅆ        2            ⁢                        B          o                ⁡                  (          t          )                            ⅆ      xdz        ,          ⁢                    ⅆ        2            ⁢                        B          o                ⁡                  (          t          )                            ⅆ      ydz      denotes the time-dependent, spatially quadratic (second order) fields.
In general, the eddy-current field patterns are complex in space and time. In most practical situations, however, it is sufficient to consider 0th and 1st order spatial terms only. The eddy-current induced field of 0th order corresponds to a residual static field (Bo) offset and results in a phase error that is constant across the image. The field of 1st order affects the gradient fields and can roughly be described in a delay in the net gradient waveform, corresponding to a linear phase ramp in image space according to the Fourier shift theorem.
One approach for eddy-current compensation includes modeling phase errors based on system specific parameters, which then leads to gradient waveform compensation based on the system specific parameters. Another approach is applied during image reconstruction. Image-based corrections are usually based on the determination of the phase of static tissue and subsequent subtraction of this residual phase or a model fitted to the residual phase from the actual data. Static tissue may be identified automatically by using magnitude-based criteria or, if time-resolved data are available, based on the variance of the image phase over time.
It would therefore be desirable to have a system and method capable of minimizing or correcting flow velocity measurements in phase contrast imaging independent of the specific source of magnetic field encoding errors.